Embedded dielectric rod antenna

ABSTRACT

A compact, directional antenna element for achieving narrow beamwidths andide bandwidths. The element is formed from a polyrod having a high dielectric constant embedded in a wave guide made of a second medium having a dielectric constant slightly lower than that of the rod.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application makes reference to a parent patent application by thesame inventors earlier filed in the Patent and Trademark Office of theUnited States on the 25th of March 1975 and is a C-I-P and assigned Ser.No. 565,292, now abandoned, for the purpose of obtaining those benefitsbestowed by 35 U.S. C. 120.

BACKGROUND OF THE INVENTION

The present invention pertains generally to electronically scannedantennas and more particularly to the polyrod type of directive antennaelement. An outstanding problem in naval fire control is thesimultaneous tracking of multiple targets. This problem is partiallysolved by the use of electronically scanned antenna arrays. Due to thecost and complexity of mutual impedance and computerized steeringcommands, the use of these arrays has been fairly limited in the fleet.

Another configuration has a series of single radar beams produced bydirective antenna elements which are serially addressed in accordancewith their placement, thereby providing a steered beam. End-firedirective antenna elements have advantages over alternative types ofbeam directors such as parabolic reflectors, lenses, and antennasubarrays since end-fire elements occupy considerably lesscross-sectional surface area. The actual length of an end-fire elementhowever, has virtually eliminated their use.

The electromagnetic waves that can exist on a dielectric rod were firstsolved by Hondros and Debye and published in the Annelen der Physik,volume 32, number 8 (1910) in an article entitled ElecktromagnetischeWellen an dielektrischen Drachen, pages 465 through 476. The generaltheory of these modes was extended by Carson, Mead, and Schelkunoff inHyper-frequency Waveguides--Mathematical Theory, BSTJ volume 15, page310 (April, 1936).

U.S. Pat. No. 2,425,336, issued on the (12th of August 1947 to G. E.Mueller describes the first application of this theory in the form of adirective dielectric antenna. Following the second World War, anelectronically steerable array of forty-two dielectric antennas wasapplied to the fire control of a U.S. Navy radar; the antenna designtheory was published by Mueller and Tyrrell in a paper titled PolyrodAntennas, BSTJ volume 26, page 837 (October, 1947). The theory was basedon the premise that the wave on the rod leaked as it traveled down therod. By varying the rod diameter and the dielectric constant of the rod,the phase of leaked radiation could be adjusted in such a manner that itadded constructively in the forward direction to produce a beam.Antennas could be designed that were reasonably close to practice aslong as the beam widths were greater than 20 degrees. Many workers inthis country and abroad have continued with this approach but failed toproduce significant advances. Following the publication by Kao,Dielectric Surface Waveguides, URSI General Assembly, Ottawa, Canada, inpaper 6-3.2, August 18 through 28, 1969 and the subsequent work in thefield of fiber optics (dielectric rods), the basic theory became widespread. This theory and the many confirming experiments havedemonstrated that the dominant electromagnetic mode used on the antennadoes not leak as it travels the rod. An alternate approach to theradiation mechanism has been developed with the electromagnetic fielddistribution existing around the distal end of the antenna regarded asan aperature. The extent of this field distribution determines theaperature size which in turn determines the far field radiation pattern.Zucker first recognized this approach (Theory and Application of SurfaceWaves, Nuovo Cimenti Suppl., volume 9, page 451, 1952); it was furtherexpanded by Yahjian and Korhauser (A Modal Analysis of the DielectricRod Antenna Excited by the HE₁₁ Mode, IEEE Transactions AP-20, number 2,page 122, March, 1972) and Zucker (Antenna Theory, Part 2, Chapter 21,McGraw-Hill, N.Y.) in the United States, Brown and Spector (Theradiating Properties of End-fire Aerials, Proceedings of the IEE, 104B,page 27, 1957) in England, and E. G. Neumann (Uber dasElectromagnetische Feld am Freiden Ende einer Dielektrischen Lietung I.Abstrahlung, Z. Angen Phys. 24, page 1, 1967) in West Germany

In studying the physical characteristics of end-fire dielectric rodantennas (i.e., "polyrods"), diffraction theory indicates that if Drepresents the maximum rod diameter and λ the responsive antennawavelength, then the minimum angle θ of the antenna beam within whichradiation can be concentrated is proportional to λ/D. To achieve smallangles, therefore, λ must be small and D large. Both λ and D areconstrained however, by other system characteristics. The wavelength, λ,is basically restricted in radar to a limited range of wavelengths.Therefore, the only method of restricting the angle θ is to increase theactual length, L_(a), of the rod. By making L_(a) large in a discreteelemental linear array and phasing the array for end fire (i.e., liningup a series of dipole elements and phasing each successive dipole by 90°so that the beam is emitted along the line of the array), thecross-sectional dimension of the array is made independent of the actuallength of the array and is restricted by only the length of a singleantenna element--usually on the order of a wavelength or less which, forI band, is about three centimeters.

Dielectric rods are ideal substitutes for the directive antenna elementsin a linear phased array since they are easily phased for end fire and,by their design, can be constructed of any one of a number of low lossdielectric materials available and easily matched for impedance over awide range of frequencies.

The half power beam-width (HPBW) of dielectric rod antenna indicatesthat: ##EQU1## Using I band (λ=3 cm), a 6° HPBW requires a rod having anelectrical length of approximately three meters (˜10 ft). Even if theHansen-Woodyard supergain relation is applied, a ten foot pole couldeither be used to produce a 4° beam or reduced to a seven foot pole toretain a 6° HPBW beam. A seven foot pole however, is still too long foruse in a phased array.

SUMMARY OF THE INVENTION

The present invention overcomes the disadvantages and limitations of theprior art by providing a short length, narrow beam-width, dielectric rodantenna element. The antenna element of the present invention comprisesa rod having a high dielectric constant surrounded by a medium having adielectric constant slightly lower than that of the rod. The result ofembedding the rod in this manner is that the electrical wavelength ofthe antenna is lengthened by the square root of the waveguide'sdielectric constant. The physical length of the antenna can therefore beshortened by the square root of the dielectric constant.

It is therefore an object of the present invention to provide animproved directive antenna element.

It is also an object of the present invention to provide a high gainantenna element.

Another object of the present invention is to provide a broad bandwidthantenna element.

Another object of the present invention is to provide a short length,narrow beamwidth, end-fired antenna element.

Other objects, advantages and novel features of the invention willbecome appararent from the following detailed description of theinvention when considered in conjunction with the accompanying drawingswherein:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a side view of a prior art polyrod design.

FIG. 1A is a cross-sectional view along the longitudinal axis of thepolyrod in FIG. 1, showing the three decibel beam pattern.

FIG. 1B is a side view showing the boundary used for solution ofMaxwell's equations to determine which electromagnetic waves can existin the vicinity of a dielectric rod.

FIG. 1C is an isometric view of a section of a cylindrical polyrodshowing the electric field lines of the dominant electromagnetic mode.

FIG. 2 is a graph showing the ratio between the diameter of a polyrodand the wavelength external to the polyrod plotted along the abscissaand the phase velocity plotted along the ordinate, to show the dominantmode dispersion curves for six different ratios between the dielectricconstant of medium 1 and that of medium 2.

FIG. 3 is a simplified replot of the graph shown in FIG. 2 with a singledispersion curve.

FIG. 4 is a simplified replot of the graph shown in FIG. 2 with a singledispersion curve graduated to show percentage of energy external to apolyrod.

FIG. 5 is a cross-sectional view adjacent to an end view, both viewsshowing the electric field distribution around a polyrod.

FIG. 6 is a graph with the ratio between the diameter of a polyrod andthe wavelength external to the polyrod plotted along the abscissa andthe percentage of energy external to the polyrod plotted along theordinate, for imaginary cylindrical surfaces of five different diameterscoaxial with the polyrod.

FIG. 7 is an isometric view of one embodiment of a polyrod end-fireelement surrounded by a second dielectric medium.

FIG. 7A is an isometric view of the polyrod shown in FIG. 7 surroundedby a second dielectric medium and a conical horn.

FIG. 8 is an isometric view of an alternate embodiment of a doubledielectric antenna.

FIG. 9 is an isometric view of an alternate embodiment of a doubledielectric antenna.

FIG. 10 is a single-line schematic of a circuit incorporating a Butlermatrix.

FIG. 11 is a single-line schematic of a circuit incorporating aninverted Butler matrix.

DETAILED DESCRIPTION OF THE EMBODIMENTS

An electromagnetic wave can be launched on a dielectric rod and utilizedas a transmission line (e.g., fiber optics) or an antenna (e.g.,polyrod). The basic equations and solutions for the existence of anelectromagnetic wave on a dielectric are well documented. FIG. 1illustrates the prior art design for a polyrod antenna. Implied is theuse of polystyrene (ε₁ =2.56) for dielectric rod 16 and excitation ofHE₁₁ mode on the rod. The beamwidth, θ_(3dB), as shown in FIG. 1A, is afunction of the length, L_(a), of rod 16 as long as L_(a) is less thannine wavelengths. Antennas with rods longer than 9λ_(o) continue to havea beam width of approximately twenty degrees. The rod diameter, D₁, is,as explained below, emperically determined to preclude excitation ofhigher order modes.

FIG. 1B is a sketch of the boundary taken between medium 1 of thepolyrod and medium 2 of the surrounding environment, in this instance,air (ε₂ =1.0), to show that electromagnetic waves can exist in thevicinity of a dielectric rod. The mathematics involved in solution ofMaxwell's equations for the boundary conditions are given in OpticalWaveguides, Chapter 4, by Kapany and Burke, Academic Press, and inPerformance of Polymer Waveguide at Milimeter Wavelengths, by Jablonski,Krall, VanSant and Syeles, NSWC/WOL TR77-115, May 1978, and will not berepeated here. FIG. 1C is a sketch of the electric field lines of thedominant HE₁₁ mode on a polyrod 16 showing how the fields exist beyondthe rod in the surrounding medium 2.

From the solutions for the various modes that can exist a dominant canbe found. Similar to the dominant mode in coaxial cables, this mode,called the hybrid or the dipole or the HE₁₁ mode, can propagate nomatter how small the rod radius is. The critical radius below which onlythe HE₁₁ can exist is given by the root of the zero order Besselfunction whose argument is: ##EQU2## where a=radius of the dielectricrod

λ₂ =wavelength in region surrounding the rod.

Equation 1 shows that the extinction of the higher order modes is afunction of the rod radius, the wavelength outside the rod, and therelative dielectric constant between the rod and its surroundings. Theguidance condition for the HE₁₁ mode is plotted in FIG. 2. Thenormalized wavelength on the rod is plotted against the normalized roddiameter as a function of various relative dielectric constants. Thedotted curve, the mode extinction curve, comes from Equation 1 and theregion to the left of it can only support the HE₁₁ mode. It can be seenfrom FIG. 2 that as the relative dielectric constant increases, theslope of the curves also increases. With an increased slope, a smallchange in driving frequency will produce a large change in phasevelocity of the wave excited on the rod. Wide band antennas therefore,should be built from low relative dielectric constant materials. In thepast, most of antennas have been fabricated from polystyrene, a materialwith a dielectric constant relative to air of about 2.5. To be able tomake comparisons we shall continue to use this value. FIG. 3 is a replotof FIG. 2 with only this value. From FIG. 3 is can be seen that forlarge diameter antennas the mode wavelength approaches asymptoticallythe wavelength it would have if traveling entirely inside the rod. Forvery small diameters the mode approaches the wavelength it would havetraveling entirely outside the rod (i.e., entirely in medium 2). Theformer is the tightly bound condition where the wave energy resideswithin or nearby the rod; it can be excited efficiently. The latter isthe loosely bound condition where energy spreads away from the rod andcouples easily to radiation modes. A polyrod antenna is designed tooperate in the region between these two extremes. The diameter may becompromised so that both excitation remains reasonably efficient and thefield extends enough to produce a reasonable aperature.

The extent of the field external to the rod is exhibited in FIG. 4. Itcan be seen from FIG. 4 that if 2a/λ₂ =0.612 (i.e., if the value of2a/λ₂ is below extinction of higher order modes), then at least 20% ofthe energy will be external to the rod. For an antenna design moreinformation than this is needed. It is necessary to know how and wherethis energy is distributed. The electric field distribution around therod is shown in FIG. 5. In general, it is necessary to create a fieldconfiguration at the launching point that is close to the desired modefield configuration if efficient excitation is to be expected. Thecross-sectional view of FIG. 5 (from Computer-Graphic Analysis ofDielectric Waveguides, IEEE Transactions, MIT, page 187, March 1967)illustrates the desired fields. The quantitative distribution of theenergy around the rod has been calculated and is shown in FIG. 6. It canbe seen in FIG. 6, just as in FIG. 4, that for a cylinder 14 of the samediameter as the rod (i.e., D.sub. 2 =2a) and for a rod of 2a/λ₂ =0.612(i.e. extinction), 20% of the energy in the wave is external to the rod.Curve 4a however, does not have an abscissa value of 2a/λ₂ =0.612 on theplot. Less than two percent of the energy is therefore external to animaginary cylinder (i.e., media 2) 14 with a diameter 4a; 18% of theenergy in the wave is between the rod and the outer diameter of theimaginary cylinder 14 while 80% is within the rod itself. A similarcalculation for smaller diameter rods reveals that the energy not onlyspreads but that its distribution is approximately binomial.

EXAMPLE 1

Consider a polyrod designed to provide a beamwidth of 20° at a frequencyof 4 gigahertz (λ_(o) =7.49 cm.). The necessary aperture may becalculated from the beamwidth and the rod diameter calculated from theaperature. Transition between the coaxial feed and the excitation end ofthe polyrod will be considered from these dimensions. Note that the 4gigahertz frequency, chosen purely on the basis of laboratoryconvenience (i.e., economy of time and funds), is more than one order ofmagnitude higher than the frequency for which a polyrod antenna islikely to be used. Scaling of frequency to lower values is consideredtrivial because theory readily allows scaling while dielectric materialas a general rule operate more favorably at lower frequencies.

For the distribution of a dipole wave (HE₁₁) on a polyrod, Neuman (i.e.,Radiation Mechanism of Dielectric Rod and Yagi Aerials, ElectronicLetters, volume 6, number 16, August, 1970) gives the directive gain as:

    D(ψ,θ)=[1+(2πr.sub.o θ/λ.sub.2).sup.2 ].sup.-2 (2)

where θ is the angle between the axis of the antenna and the observationpoint, and independence of angle ψ is assured by mode symmetry. Thevariable r_(o) determines the extent of the surface wave across theassumed aperature at the end of the dipole. From (2) the 3 dB beamwidthin degrees can be calculated as: ##EQU3## for a 20° beamwidth and awavelength in medium 2, assuming medium 2 to be air, of 7.49centimeters, equation (3) yields r_(o) =4.38. The value of r_(o) isdirectly connected to the wave numbers in medium 1 and 2 through therelationship: ##EQU4## Solving this equation for λ₁ /λ₂ =0.965 yieldsthe phase velocity that is needed to enter the dispersion curve of FIG.3. From this value, curve in FIG. 3 indicates that the required roddiameter is 2a=0.34λ₂ =2.5 cm.

As a check on these results, 2a/λ₂ =0.34 is entered on FIG. 6 to whichshow that less than 1% of the mode energy is external to an imaginarycircle whose diameter is 25 centimeters and coaxial with rod 16. If thedistribution of FIG. 6, which is nearly binomial, is used to calculatethe half-power beamwidth, then: ##EQU5## This confirms the originalcalculation.

The diameter of the polyrod antenna at 4 gigahertz is now fixed at 2.5centimeters, as shown in the sketch in FIG. 7. If the HE₁₁ mode could beexcited from a source of 4 gigahertz on a short section of the rod with100% efficiency, the design would be finished. Unfortunately, it is notpossible. Efficiency of excitation from common transmission lines canreach values as high as 80%. This is done with rod diameters differingfrom that calculated to produce a 20° beamwidth. The transition fromexcitation diameter to radiation diameter must be done with care becauseit is possible to radiate unwanted patterns if care is not taken. Thelength of the antenna is determined so as to avoid this effect. Therehas been some theoretical work which predicts efficiencies of excitingthe HE₁₁ mode on a polyrod of between 63% to 80%. Experimentally, mostof the polyrods have been excited from rectangular waveguides and havereported efficiencies of between 84% to 90%. Referring now to FIG. 7A, aside view of a polyrod designed with those dimensions calculated inExample 1 and shown in FIG. 7, we shall follow Schulten (Applications ofa Dielectric Line, Phillips Technical Review, volume 26, number 11, 12page 350, 1965) who starts with a tapered rod in a rectangularwaveguide, section 16a, makes a transition to a circular waveguide,section 16b, and then to a conical horn, section 16c. It has been ourexperience that the VSWR in the waveguide can be held below 1.1throughout the guide bandwidth. The transition to circular guide TE₁₁mode from the rectangular TE₀₁ mode aids in orienting the maximumelectric field lines in coincidence with those of the dielectric HE₁₁mode shown in FIG. 5. The conical horn will be extended with a 20° flareangle until its aperature is 25 centimeters diameter to provide a smoothtransition and eliminate back radiation. The value 25 centimeters wasdetermined by the 99% energy aperature criterion.

For maximum efficiency of mode excitation, Yip (Launching Efficiency ofthe HE₁₁ Surface Mode on a Dielectric Rod Waveguide, IEEE TransactionsMIT-18, number 12, page 1033, December 1970) choose 2a/λ₂ =0.5 requiringa rod diameter of 3.7 centimeters. An abrupt transition from thisdiameter to 2.5 centimeters at the radiation end would cause undesiredradiation. A gradual taper will reduce this undesired radiation. Sincethe fields are more loosely coupled at small diameters however, it isreasonable to expect that a linear taper, in a region of small diameter,will produce greater radiation than would the same linear taper in aregion of large diameters. The solution is to use an exponential taperwith the greatest change on the taper occuring at the largest diameter.The radiation losses can then be made as small as desired simply byextending the length of the taper. The problem here is to choose thesmallest possible antenna length. With a transition length L_(t) =10λ₂=75 centimeters, the relative losses of the exponential taper, comparedto an abrupt step, are down about 10 dB. Under the foregoing choices,the exponential taper is given in the form:

    a(Z)=1.25+0.60e.sup.-.0.06Z                                (6)

With this information the basic antenna design is complete. In FIG. 7Aan absorber 22 and a cap (quarter-wave transformer) 18 on the end ofpolyrod 16 have been added. Since ninety-nine percent of the power iswithin a twenty-five centimeter diameter of the longitudinal axis of rod16, the absorber will only affect the remaining one percent of the powerof the desired mode. Power in the circular waveguide that is nottransformed into the HE₁₁ mode, about fifteen percent, will also radiateand cause sidelobes in the main beam pattern. The absorber is used toeliminate much of this power. The end cap 18 on the polyrod is normallyabsent from prior art end-fire directive antenna design. FIG. 6 however,indicates that approximately twenty-five percent of the energy is withinrod 16; to avoid unwanted reflections at the end, quarter-wavetransformer 18 is installed as a matching section.

The total losses expected in the antenna shown in FIG. 7A are less than2 dB. At the coaxial transition to rectangular waveguide, usingcommercially available equipment, the VSWR is less than 1.25. Thetapered dielectric will not increase this appreciably. Therefore, lessthan 2% of the energy should be lost. At the circular waveguide todielectric mode conversion at least 80% efficiency is expected (20%loss). The absorber will take 1% from the fields of the mode and thedielectric losses due to displacement currents amount to less than 1%. Atotal of these factors is between 1 dB and 2 dB.

For the benefit of those unacquainted with the electrical arts and moreparticularly, with the distinctions between those materials classifiedas insulators and conductors and those materials having electricalproperties which allow them to be characterized as dielectric, thefollowing table of exemplary dielectric materials is set forth.

                  TABLE                                                           ______________________________________                                                   Dielectric    Loss                                                            Constant      Tangent × 10.sup.4                             ______________________________________                                        TiO.sub.2    ˜100      5.2                                              BaTiO.sub.2   ˜1200    75-500                                           CaTiO.sub.2  ˜167      3.1                                              SrTiO.sub.2  ˜225      1.0                                              BaTi.sub.9 O.sub.20                                                                        ˜50       200                                              79%(BaTi.sub.9 O.sub.20)                                                                   ˜800      700                                              21%(SrTiO.sub.2)                                                              Distilled Water                                                                            87-55            0.04                                            Sea Water    76-70           100                                              Ceramic NPOT96                                                                             29.5            12-2                                             (American Lava Co.)                                                           MgTiO.sub.2  13.9            15-5                                             Glycol       37.7            0.224                                            Nitrobenzene 34.8            0.225                                            ______________________________________                                    

These values listed are for frequencies on the order of 10⁸ Hertz. Amore complete list of dielectric materials suitable for construction ofthe double dielectric antenna disclosed here is compiled in DielectricMaterials and Applications by A. R. vonHippel, Technology Press ofM.I.T. and John Wiley & Sons, as well as in the CRC Handbook ofChemistry And Physics. The moisture absorption of these materials istypically either zero or negligible. It is a well known technique tovary the composition of mixtures such as those listed in the Table, andthereby change the dielectric constant.

EXAMPLE 2

The polyrod just considered and the accompanying theory were in terms ofthe parameters ε₁ /ε₂ and λ₁ /λ₂. If ε₁ and ε₂ are now changed with theratio ε₁ /ε₂ fixed, the wavelengths change. By choosing ε₁ =25 and ε₂=10 (e.g., lead monoxide, ε₁ ≃25.9 and aluminum oxide, ε₂ ≃10.0,respectively, or alternately, two different volume-percentage mixturesof rutile), wavelength λ₂ is reduced by 3.16, the square root of ε₂.Referring back to FIG. 2 where the electric field lines are shown asexisting beyond rod 16 (i.e., medium 1) and into the surrounding medium2; it is this phenomenon that permits control of the wavelength size,λ₂, by the external medium 2. The amplitude of the wave dies off withdistance from the center of the rod, thereby allowing for a design offinite extent with an external medium other than air. The dimensionsderived for the polyrod shown in FIG. 7 where determined for a medium 2with a dielectric constant of 1.00; if medium 2 is changed to a materialwith a dielectric constant of 10 and substituted for the air used inExample 1 to fill the twenty-five centimeter radius of cylinder 14, thedevice shown in FIG. 7 will effectively become a double dielectricantenna and all dimensions given will be reduced by a factor equal tothe square root of ten. There are two differences between the polyroddiscussed earlier and the double dielectric antenna proposed here.First, the mode energy is largely contained in medium 2, a material witha dielectric constant of ten, and must be matched to air to assureefficient radiation. A quarter-wave matching plate 18 must be enlargedto cover the distal ends of both polyrod 16 and cylindrical sheath 14 ofmedium 2. Second, the losses of the antenna change because of thepresence of the dielectric material surrounding the rod. Attenuation onthe antenna is given by equation (6), a modification of an equationpublished in Attenuation in a Dielectric Circular Rod, by W. Elsasser inJournal of Applied Physics, volume 20, page 1192 in December, 1949, thatis modified to fit a double dielectric antenna. ##EQU6##

Inserting appropriate values for the materials that are to be used inconstructing an antenna into this equation yields an attenuation of 4decibels per meter. Since the length of the antenna has been reduced tosomething close to one-third of a meter, the total of the additionalloss caused by the presence of sheath 14 amounts to 1.3 decibels. Thisfactor could become larger for very high dielectric materials with largeloss tangents (i.e., tan δ). A compromise between antenna length and theextra radiation accompanying the length would then be in order. For thisdesign however, the additional loss is insignificant.

The use of a quarter wave plate is expected to produce its effect on theoverall bandwidth of the antenna. Again, it is used as a matter ofconvenience and wider bandwidth matching circuits could be used.Alternately, a Chebyschev impedance transformer could be installed inorder to match the end of double dielectric antenna to the atmosphere.

EXAMPLE 3

FIG. 8 discloses the elements of another embodiment of a directiveantenna dielectric end-fire polyrod. A linearly tapered feed 10 supplieda radar signal across the ground plane 12 to the antenna elementconstituting a waveguide 14 and rod 16. The signal supplied by taperedfeed 10 must be of the proper mode as, for example, the HE₁₁ mode todetermine phase velocity and construct the rod 16 in the proper mannerto cause end fire.

The effect of the waveguide 14 is to slow the propagation of the signaloutside the rod. The wavelength λ.sub.ε within any dielectric is equalto the wavelength in free space λ_(o) divided by the square root of thedielectric constant ε of the material. Thus: ##EQU7##

In the described embodiment then, where the dielectric constant ofmedium 2 (i.e., sheath 14) surrounding dielectric rod 16, has beenselected as 81, the wavelength of the radar signal in the waveguide isreduced by a factor of 9.

Considering the HPBW equation again, the physical length of the rod isreduced by a factor of 9 since the length of the rod must be measured inwavelengths in the medium surrounding the rod and the wavelengths in thedielectric waveguide are 1/9 their length in free space. The ten footpole of the prior art (dielectric rod 16) can therefore, if surroundedby a dielectric material having a dielectric constant equal to 81, bereduced in actual length to a rod just over a foot long while retainingits ten foot electronic length. Of course, material having higherdielectric constants can be used to even further reduce the length ofthe rod.

As also shown in FIG. 8, the antenna element has a quarter waveimpedance matching transformer 18' which couples the antenna to theatmosphere for end fire. The transformer is one quarter wave lengththick and has a dielectric constant equal to the square root of theproduct of the two mediums being matched, (i.e., the waveguide and theatmosphere). Since the atmosphere has a dielectric constant of 1, thedielectric constant of the transformer is 9.

The cross-sectional dimension of the antenna element including thewaveguide has been selected to provide -40 dB mutual coupling with otherantennas spaced one wavelength apart. Studies have shown that thiscoupling is provided by a crosssectional dimension of λ_(o) /3 which forI band would be about 1 centimeter, although smaller cross-sectionaldimensions would most probably be acceptable. The diameter of rod 16equals λ/20. The actual length of rod 16 equals 10λ.sub.ε. Ground plane12, shown partially cut away in FIG. 8, serves to image the radiatingstructure of double the dielectric antenna, mainly by suppressing theback lobe of the beam pattern. Without ground plane 12, the doubledielectric antenna would have a back lobe at about -40 decibels down.

The structure shown in FIG. 8 has a polyrod 16 (medium 1) with adielectric constant of 84, embedded in a sheath 14 (medium 2) with adielectric constant of 81; it has a relative dielectric constant of1.04. One material suitable for polyrod 16 is Ceramic N750T96, a ceramiccommercially available from American Lava Company, (ε₁ =83.4 between1×10² through 1×10¹⁰ Hertz while tan δ varies from 5.7 to 14.6 over thesame frequency range); sheath 14 could be made of the same material in aless concentrated mixture so as to reduce the dielectric constant to 81over the band of intended use. Alternately, sheath 14 could be a liquidsuch as distilled water (ε₂ =78 and tan δ=0.005 at 10⁸ Hertz). If sheath14 is made from a material in a gaseous or liquid phase rather than onein a solid phase, an additional component, namely a container 19, isnecessary to confine the medium 2 to the vicinity of polyrod 16.Although container 19 serves no function other than that of confining agaseous or liquid phase medium 2, if made of a conducting material(e.g., steel, aluminum), container 19 would tend to act as a cylindricalhorn. As shown by FIG. 6, antennas designed for the region between theloosely bound and tightly bound conditions, very little wave energywould be influenced by a metal container 19. Additionally, container 19may be made of a non-conducting material such as polyethylene. As noelectrical function is contemplated for container 19, its thickness isprimarily determined by design convenience.

One major advantage of the antenna element of the embodiment describedis its broad bandwidth. Referring to FIG. 2, phase velocity is plottedagainst the rod diameter for materials having various relativedielectric constants in response to only one particular excitation mode.Inherent constraints of the physics of the antenna element and thefrequency require the phase velocity in the dielectric rod to approach100% of its velocity in the waveguide for high gains in the antenna.Relative dielectric constants are determined in the antenna of thepreferred embodiment by taking the ratio of the dielectric constant ofthe rod to that of the waveguide. A dielectric rod having a dielectricconstant of 9 (ε₁ =10) without a surrounding waveguide would thanproduce a relative dielectric constant of 9 (ε_(r) =9) such as plot 9,FIG. 2, since the dielectric constant of air is approximately equal to 1(ε=1). The bandwidth of such an antenna element would be very narrowsince slight changes if λ_(o) (i.e., if medium 2 is air, λ_(o) =λ₂) asshown in FIG. 2 would cause great changes in the phase velocity andtherefore in gain of the antenna.

As shown in FIG. 2, however, relative dielectric constants whichapproach 1 have very flat responses, asymptotically, approaching arelative phase velocity of 1 which renders high gain antennas with broadbandwidths, clearly an advantageous trait for radar antennas. Forexample, once a relative dielectric constant of 1.04 (ε_(r) =1.04)produced by the exemplary embodiment of the present invention is fixed,the wavelength could vary considerably in the horizontal axis,indicating broad bandwidth, and remain within the constraints of thenecessary phase velocity for a properly sized rod having very high gain.So the closely matched high valued dielectric constant of the dielectricwaveguide not only allows the antenna to be shortened considerably, butrenders it a very high gain antenna with broad bandwidth.

EXAMPLE 4

Consider now a double dielectric antenna designed for three hundredmegahertz (λ_(o) =1 meter). Rod 16 is made of strontium titanate (ε₁=232, tan δ=2×10⁻⁴) while sheath 14 is made of calcium titanate (ε₂=169, tan δ=1×10⁻⁴). Using equation (7), λ₂ =7.7 centimeters.Arbitrarily selecting a rod length of six times the wavelength in medium2, (6λ₂), both rod 16 and sheath 14 have a length of 46 centimeters (18inches). The relative dielectric constant between the two materialequals 1.39. Selecting the value of D₁ /λ₂ at about 0.8 yields a roddiameter of 6 centimeters (2.5 inches). If gain is set at 40, then:##EQU8## or the diameter of sheath 14 is 15.5 centimeters (6.1 inches).For the quarter-wave transformer 18, ##EQU9##

The length (i.e., "thickness") of transformer 18 is 7 centimeters or2.75 inches; the width equals the width of sheath 14, about 6.1 inches.A sketch of the embodiment displaying these dimensions is given in FIG.9.

To scan a system of end-fire directive antenna elements, a variation ofthe Butler matrix is useful. A standard Butler matrix is shown in FIG.10. It comprises an array of hybrid couplers and fixed phase shiftersthat have an equal number of binary inputs and outputs. In its usualmode, a linear array of antenna elements 30 are connected to the outputterminals. When a microwave power source 32 is connected to one of theinput terminals, the matrix distributes the power to all of the outputswith a linear phase shift between adjacent terminals. As the powersource is connected to other inputs, the only change in output is theamount of phase shift that exists between adjacent terminals whichdetermines the angle of the output beam. Thus the matrix is capable ofproducing 2^(n) distinct beam positions in space from the antenna arrayand each position is uniquely defined by a predetermined input position.Now consider FIG. 11, where the same Butler matrix has been inverted orreversed.

Each of the outputs of the inverted Butler matrix of FIG. 11 is nowconnected to a coherent power source 34 whose phase can be adjustedelectronically. Now, for a given linear phase shift between theoscillators, all of the power of the individual oscillators can besummed to appear at one antenna port of the array of antennas 36. Bychanging the phase shift, alternate or multiple ports can be selected.In each of the antenna ports is terminated by a narrow element beamantenna element such as the one disclosed above, these beams can bephysically positioned to point anywhere in space. The antennas have nodependence on one another and can therefore be mounted in a completelyarbitrary manner. The physical destruction of any group of antennasresults in a loss of communication only from its assigned spacecoverage. A loss of any of the low powered input oscillators results ininsignificant operational output changes but could easily be detectedand pinpointed. While the butler matrix has been used as anillustration, a switching matrix would operate equally well and at firstsight appears less cumbersome. The n-multiple oscillators are also notnecessary but were included to illustrate how low-powered, solid stateoscillators might be included. The problem of mutual impedance and ofcomplex steering commands of the prior art devices therefore disappearscompletely in this arrangement.

Obviously many modifications and variations of the present invention arepossible in light of the above teachings. For example, the element maybe used for either transmission or reception, depending upon theparticular use desired. In addition, various materials whether in asolid, liquid or gaseous phase, having different dielectric constantsthan those shown in the exemplary embodiments, may be used for thedielectric rod and for the surrounding sheath. If the sheath is a soliddielectric material for example, it would serve quite suitable as acontainer for either a gaseous or liquid phase polyrod material.

Radiation is nearly isotropic about the axis of polyrod 16, regardlessof whether the cross-section of polyrod 16 is octagonal, square,rectangular, or round. The important design criterion is the avoidanceof abrupt transition along the longitudinal surface of polyrod 16;assuming the cross-section of polyrod 16 to be not constant with itslength, the dimension of the cross-section must make a smooth or taperedtransition between the waveguide feed 10 and the distal end. If thiscriterion is met, polyrod 16 may have any cross-sectional shape, whetheroctagonal, rectangular, triangular or round. Similarly, thecross-sectional shape of sheath 14 is not a primary designconsideration. If thick enough (e.g., D₂ ≧4a), the cross-sectional shapeof sheath 14 may even be made irregular without significantly affectingperformance of a double dielectric antenna. As might be expected, afteran examination of FIG. 6, a double dielectric antenna constructed with apolyrod embedded in a measurable thickness of a material forming medium2, (i.e., sheath 14) having a slightly lesser dielectric constant willprovide a narrower beamwidth than one constructed with the same polyrodcoated with just a few microns thickness with the same medium 2. Thedistal end of polyrod 16 may be in intimate contact with thequarter-wave transformer 18, 18' or may be separated by a fractionalthickness of medium 2 from transformer 18, 18'.

It is therefore to be understood that within the scope of the appendedclaims the invention may be practiced otherwise than as specificallydescribed.

What is claimed as new and desired to be secured by Letters Patent ofthe United States is:
 1. An end-fired antenna element for projecting anarrow beam of energy into the surrounding environment, comprising:feedmeans terminating in an aperature; a dielectric rod of a material havinga dielectric constant ε₁ coupled to the aperture and extendinglongitudinally therefrom; a dielectric material surrounding saiddielectric rod along the length thereof having a dielectric constant ε₂≧81 and substantially greater than the dielectric constant of theenvironment but less than the dielectric constant ε₁.
 2. A directiveantenna element, comprising:feed means for delivering a single modeelectromagnetic signal; a rod connected to the feed means, constructedof a material having a first dielectric constant; cylindrical materialmeans mounted in the atmosphere and surrounding said rod and constructedof a material having a second dielectric constant ε₂ greater than thedielectric constant of the atmosphere but less than the first dielectricconstant and the value of the second dielectric constant being not lessthan eight-one.
 3. An antenna element as set forth in claims 1 or 2wherein said dielectric rod has an actual length L_(a) and an effectivelength L_(e) determined by the formula L_(e) =L_(a) √ε₂.
 4. An end-firedantenna element, comprising:feed means for delivering a single modeelectromagnetic signal; a rod of a first material having a dielectricconstant, ε₁, electrically coupled to the feed means; a sheath of asecond material having a dielectric constant, ε₂, greater in value thanten but lesser in value than ε₁, surrounding the rod; a quarter waveimpedance matching transformer coupling the antenna element to thesurrounding environment for end fire, said transformer having adielectric constant equal to the square root of the product of thedielectric constants of the second material and the surroundingenvironment; wherein the ratio ε₁ /ε₂ ≧3.0.
 5. The antenna set forth inclaim 4 wherein ε₂ ≧25.
 6. The antenna set forth in claim 4 wherein ε₂≧30.
 7. The antenna set forth in claim 4 wherein ε₂ ≧50.
 8. The antennaset forth in claim 4 wherein ε₂ ≧81.
 9. A polyrod antenna element havinga half-power beamwidth θ, in a surrounding environment comprising:feedmeans terminating in a aperture; a dielectric rod of effective length Lextending longitudinally from the feed means and having a dielectricconstant ε₁, wherein the effective length is defined by the equation##EQU10## a dielectric medium surrounding the rod having a dielectricconstant ε₂ less than ε₁, but substantially greater than the dielectricconstant of the surrounding environment, such that: ##EQU11## wherebythe actual length L_(a) of the rod is defined by the equation: ##EQU12##a quarter wave impedance matching transformer coupling the antennaelement to the surrounding environment for end fire, said transformerhaving a dielectric constant equal to the square root of the product ofthe dielectric constants of the dielectric medium and the surroundingenvironment.
 10. A polyrod antenna element having a half-power beamwidthθ in a surrounding environment, comprising:feed means terminating in anaperture; a dielectric rod of effective length L extendinglongitudinally from the feed means and having a dielectric constant ε₁,wherein the effective length is defined by the equation ##EQU13## adielectric medium surrounding the rod having a dielectric constant ε₂less than ε₁ but substantially greater than the dielectric constar ofthe surrounding environment, such that: ##EQU14## whereby the actuallength L_(a) of the rod is defined by the equation: ##EQU15## a quarterwave impedance matching transformer coupling the antenna element to thesurrounding environment for end fire, said transformer having adielectric constant equal to the square root of the product of thedielectric constants of the dielectric medium and the surroundingenvironment.
 11. The antenna element set forth in claims 9 or 10 whereinε₁ ≧10.
 12. The antenna element set forth in claims 4, 9 or 10 whereinε₁ ≧25.
 13. In a directive antenna element of the type having in itsenvironment a characteristic three-decibel beamwidth and using adielectric rod of length L and dielectric constant ε₁, extendinglongitudinally from feed means terminating in an aperture, the antennaelement comprising:material of dielectric constant ε₂ surrounding therod wherein the material is selected according to the formula: ##EQU16##where ε₂ is substantially greater than the dielectric constant of theenvironment and the value of ε₂ ≧81.
 14. The antenna element set forthin claims 1, 2, 4 or 13 further comprising the dielectric materialsselected in accordance with the formula: ##EQU17##
 15. The antennaelement set forth in claims 1, 2, 4 or 13 further comprising thedielectric material selected in accordance with the formula: ##EQU18##16. The antenna set forth in claims 1, 2, 4, 9, 10 or 13 comprising:thedielectric rod having a cross-section normal to its greatest dimensionthat tapers away from the feed means.
 17. The antenna set forth in claim16 further comprised of the taper being linear.
 18. The antenna setforth in claim 16 further comprised of the taper being exponential. 19.The antenna set forth in claim 16 further comprised of the taper beingdescribed by the formula:

    a(z)=1.25=0.60e.sup.-0.62,

where a is a cross-sectional dimension and z is a longitudinaldimension.
 20. The antenna set forth in claims 4 or 13 wherein thedielectric material surrounding the dielectric rod separates thedielectric rod from a surrounding environment.
 21. The antenna set forthin claims 1, 9, 10 or 13 wherein the surrounding environment comprisesatmosphere.
 22. The antenna set forth in claim 1, 9, 10 or 13 whereinthe surrounding environment comprises water.
 23. The antenna set forthin claim 14 wherein the dielectric material surrounding the dielectricrod separates the dielectric rod from a surrounding environment.
 24. Theantenna set forth in claim 14 wherein the surrounding environmentcomprises atmosphere.
 25. The antenna set forth in claim 14 wherein thesurrounding environment comprises water.